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On the covering dimension of subspaces of product of Sorgenfrey lines


Author: Ali A. Fora
Journal: Proc. Amer. Math. Soc. 72 (1978), 601-606
MSC: Primary 54F45
DOI: https://doi.org/10.1090/S0002-9939-1978-0509262-1
MathSciNet review: 509262
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Abstract | References | Similar Articles | Additional Information

Abstract: Let S denote the Sorgenfrey line. Then the following results are proved in this paper:

(i) If X is a nonempty subspace of $ {S^{{\aleph _0}}}$, then $ \dim X = 0$.

(ii) For any nonempty separable space $ X \subset {S^{{\aleph _0}}},\dim {X^m} = 0$ for any cardinal m.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0509262-1
Keywords: Completely regular, cozero cover, cozero set, N-compact, order of a cover, Tychonoff
Article copyright: © Copyright 1978 American Mathematical Society